For a particle of mass $m$ moving with velocity $v$, what is the magnitude of its momentum $\left|p\right|$?

• A. $m+v$
• B. $mv$
• C. $\frac{m}{v}$
• D. $\frac{v}{m}$

Answer: (B)

Verified step by step guidance

1. Recall the definition of linear momentum for a particle, which is the product of its mass and velocity.
2. Express the momentum \( \mathbf{p} \) as \( \mathbf{p} = m \mathbf{v} \), where \( m \) is the mass and \( \mathbf{v} \) is the velocity vector.
3. Since the problem asks for the magnitude of the momentum, take the magnitude of both sides: \( |\mathbf{p}| = |m \mathbf{v}| \).
4. Because mass is a scalar and velocity is a vector, the magnitude of the momentum is the product of the mass and the magnitude of the velocity: \( |\mathbf{p}| = m |\mathbf{v}| \).
5. Therefore, the magnitude of the momentum is given by \( |\mathbf{p}| = m v \), where \( v \) is the speed (magnitude of velocity).